1983 KZ750 L3 tach woes

I am assuming that the tach gets its signal from the black wire according to what i can figure out from fumbling with a wire diagram.  My question is am i on track with possible finding the fault thats causing this tach to bounce all around?  Just what should i check and how do i go about eliminating things?  Bike runs great and idles smooth. Running on all 4 cylinders.  I was thinking the brown wie is a hot wire as it looks like it connects to many components.

Maybe bad connection or wire at the plug off the harness?

I had a similar problem on my 1100 unitrack. Needle was bouncing around just off tickover.

Never did get to the root of the problem - checked the wiring over and stripped the tach down.

Ended up just replacing the whole tachometer. Works fine now, so I'm guessing it wasn't the wiring feed that was at fault.